Question: Simplify the following expression: $y = \dfrac{20q}{40q + 65}$ You can assume $q \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $20q = (2\cdot2\cdot5 \cdot q)$ The denominator can be factored: $40q + 65 = (2\cdot2\cdot2\cdot5 \cdot q) + (5\cdot13)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $y = \dfrac{(5)(4q)}{(5)(8q + 13)}$ Dividing both the numerator and denominator by $5$ gives: $y = \dfrac{4q}{8q + 13}$